1
JEE Main 2021 (Online) 20th July Evening Shift
+4
-1
Let P be a variable point on the parabola $$y = 4{x^2} + 1$$. Then, the locus of the mid-point of the point P and the foot of the perpendicular drawn from the point P to the line y = x is :
A
$${(3x - y)^2} + (x - 3y) + 2 = 0$$
B
$$2{(3x - y)^2} + (x - 3y) + 2 = 0$$
C
$${(3x - y)^2} + 2(x - 3y) + 2 = 0$$
D
$$2{(x - 3y)^2} + (3x - y) + 2 = 0$$
2
JEE Main 2021 (Online) 20th July Morning Shift
+4
-1
Out of Syllabus
Let the tangent to the parabola S : y2 = 2x at the point P(2, 2) meet the x-axis at Q and normal at it meet the parabola S at the point R. Then the area (in sq. units) of the triangle PQR is equal to :
A
$${{25} \over 2}$$
B
$${{35} \over 2}$$
C
$${{15} \over 2}$$
D
25
3
JEE Main 2021 (Online) 17th March Evening Shift
+4
-1
Out of Syllabus
Let L be a tangent line to the parabola y2 = 4x $$-$$ 20 at (6, 2). If L is also a tangent to the ellipse $${{{x^2}} \over 2} + {{{y^2}} \over b} = 1$$, then the value of b is equal to :
A
20
B
14
C
16
D
11
4
JEE Main 2021 (Online) 16th March Evening Shift
+4
-1
Out of Syllabus
Let C be the locus of the mirror image of a point on the parabola y2 = 4x with respect to the line y = x. Then the equation of tangent to C at P(2, 1) is :
A
x $$-$$ y = 1
B
2x + y = 5
C
x + 3y = 5
D
x + 2y = 4
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